Q55. - Algebra 1

Question

Washington High School and McKinley High School are competing in an academic challenge. The team with a correct response is awarded 10 points. An incorrect response has a point value of $-10$. There are 5 mathematics questions

1. Write an equation that represents the scoring for the challenge.
2. Make a table of values for the possible points that a school could receive during the mathematics portion of the challenge.
3. Write about how absolute values can be used in classes other than math.

Step-by-Step Solution

Answer

1. The equation that represents the scoring of the challenge is $20x-50$.
2.  The table of the possible values that a school can receive is: -
   
   

Number of x correct questions.	Points $\left(20x-50\right)$
0	$-50$
1	$-30$
2	$-10$
3	10
4	30
5	50

 

c. In a science class, absolute value can be used for the tolerance range of pollution of plants.

Part a. Step 1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation, constants are the values that are fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Part a. Step 2. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means a positive value of that quantity.

Example: -

Consider a variable x. Here x can be both positive or negative but $\left|x\right|$ will always be positive and hence the absolute value. 

Part a. Step 3. Solution along with the given information.

It is given that there are a total of 5 questions and 10 points are awarded for correct response and the incorrect response has a point value of $-10$.

Let x be the number of correct responses and $5-x$ is the number of incorrect responses.

Therefore, the score is represented by the equation-

$$\begin{gathered} 10x-10\left(5-x\right)=10x-50+10x \\ =20x-50 \end{gathered}$$ 

Hence the equation that represents the scoring of the challenge is $20x-50$.

Part b. Step 1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation, the constants are the values that are fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Part b. Step 2. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means a positive value of that quantity.

Example: -

Consider a variable x. Here x can be both positive or negative but $\left|x\right|$ will always be positive and hence the absolute value.

Part b. Step 3. Table for the possible values of the score.

The equation that represents the scoring of the challenge is $20x-50$.

Since there are a total of five questions, so, the value of x will vary from 0 to 5.

The table of the possible values that a school can receive is: -.

 

Number of x correct questions.	Points $20x-50$
0	$-50$
1	$-30$
2	$-10$
3	10
4	30
5	50

 

Part c. Step 1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation, the constants are the values that are fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Part c. Step 2. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means a positive value of that quantity.

Example: -

Consider a variable x. Here x can be both positive or negative but $\left|x\right|$ will always be positive and hence the absolute value.

Part c. Step 3. Range.

The absolute values equation evaluates the range in which the solution of the particular equation will fall.

In a science class, the absolute value can be used for the tolerance range of pollution of plants.